Mel,
Thats an interesting question. In my opinion, running ozone at a low dose (like people do with reef tanks in order to enhance water quality) will no doubt kill some Cryptocaryon tomites that happen to get exposed to the ozone stream through the external reactor. However, like UV, this low level of ozone will have no effect on the trophonts living out in the tank on the fish. So - the fish could still develop an acute infection.
If you elevate the ozone level to "nuke" you can kill just about any living thing contained in the water flow through the reactor, but you must be certain that any excess ozone is neutralized (by using carbon or extending the contact time) before that water is returned to the aquarium. However, this will still have no effect on the trophonts attached to the fish themselves.
Ultimately, I feel that ozone use can only partially control Cryptocaryon through enhancing water quality, which in turn can help boost the fish's resistance to this parasite.
One other use for ozone is in "batch processing" - where water is removed from the tank, hit with high levels of ozone, and then de-ozonated, and then stored for later use in another system - this would eliminate Cryptocaryon for that use. I discuss that technique in my book "Advanced Aquarium Techinques" that is due out through TFH this month. One problem with ozone is that in high concentrations, in contact with seawater containing bromine, it produces ozone oxidants that persist for long periods of time. These can prove toxic unless they are eliminated by using sodium thiosulfate. (or possibly carbon filtration)
Jay Hemdal